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Gene Regulatory Networks Under Positive Feedback

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Analysis of Deterministic Cyclic Gene Regulatory Network Models with Delays

Part of the book series: SpringerBriefs in Electrical and Computer Engineering ((BRIEFSCONTROL))

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Abstract

In this chapter, we consider the simplified GRN model, with the assumption that it is under delayed positive feedback. By analyzing the fixed points of a single function determined from the nonlinear connections, we show that the system may have three equilibrium points in the positive cone. When the system has a unique equilibrium, generically all solutions converge to this point. When there are three equilibrium points, the system shows a bistable behavior. Homogenous GRNs under delayed positive feedback are analyzed, and their stability and bistability are determined from the parameters of the Hill function used in the nonlinear coupling.

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Authors and Affiliations

  1. Department of Bioengineering, University of Texas at Dallas, Richardson, TX, USA

    Mehmet Eren Ahsen

  2. Electrical and Electronics Engineering, Bilkent University, Ankara, Turkey

    Hitay Özbay

  3. Laboratoire des Signaux et Systèmes, CNRS - Centrale Supelec - Université Paris-Sud, Gif sur Yvette, France

    Silviu-Iulian Niculescu

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  1. Mehmet Eren Ahsen
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  2. Hitay Özbay
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  3. Silviu-Iulian Niculescu
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Ahsen, M.E., Özbay, H., Niculescu, SI. (2015). Gene Regulatory Networks Under Positive Feedback. In: Analysis of Deterministic Cyclic Gene Regulatory Network Models with Delays. SpringerBriefs in Electrical and Computer Engineering(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-15606-4_6

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  • DOI: https://doi.org/10.1007/978-3-319-15606-4_6

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